Unsteady flow of viscous electron fluids at abrupt appearance of electric potential gradient

This study presents an unsteady model of the electron fluid flow developed for the first time. Documented in the paper are results of analytical and numerical simulations of the hydrodynamic flow of electrons in the case of an abrupt appearance of an electric potential gradient in flat and circular conductors. The solutions are obtained analytically using the Laplace transform method and numerically using the Lattice Boltzmann method (LBM). Unsteady electric current profiles in flat and circular conductors are presented as infinite series. Theoretical results are confirmed by comparison with experimental data. A dimensionless criterion for the implementation of ballistic and hydrodynamic regimes is obtained. It is shown that, in the hydrodynamic mode, the reduction of collisions leads to a decrease in the resistance of the conductor.